Just a note...supermarkets used to stock hard boiled eggs in the shell.
I bought them for convenience sakes.
The hard shelled eggs were not top shelf quality to begin with and some were icky. So...now you can buy them peeled... packaged in nitrogen filled plastic pouches. I'm saying that's an improvement. BTW, being nitrogen filled, the peeled eggs DO last a month in the fridge, in those pouches, if they aren't opened.

After you break the pouch open and the nitrogen is released, they only last a few days if you don't wrap those peeled eggs up tight with plastic wrap.